Before searching online, check the back of your book. Pinter includes solutions or hints for roughly . These are usually the odd-numbered exercises or the most fundamental proofs needed to move on to the next chapter. 2. GitHub Repositories (The "Golden Standard")
In particular, for $$a = 0_R2$$, we have: pinter abstract algebra solutions
Abstract algebra is a "mental muscle" subject. If you look at the solution too early, you lose the opportunity to build the intuition required for higher-level math. Before searching online, check the back of your book
The First Isomorphism Theorem is a major hurdle. The First Isomorphism Theorem is a major hurdle
Many proofs in Pinter rely on a specific "trick" (like multiplying by an inverse or choosing the right mapping). Read just the first step of the solution, then close it and try to finish the proof yourself.